In this paper, we present a deep learning-based numerical method for approximating high
dimensional stochastic partial differential equations (SPDEs). At each time step, our method …

In this article, we are interested in solving numerically backward doubly stochastic
differential equations (BDSDEs) with random terminal time τ. The main motivations are …

In this paper, we first prove existence and uniqueness of the solution of a backward doubly
stochastic differential equation (BDSDE) and of the related stochastic partial differential …

Our goal is to solve certain dynamic programming equations associated to a given Markov
chain X, using a regression-based Monte Carlo algorithm. More specifically, we assume that …

In this article, we propose a wellposedness theory for a class of second order backward
doubly stochastic differential equation (2BDSDE). We prove existence and uniqueness of …

In this paper, we consider a class of backward doubly stochastic differential equations
(BDSDEs for short) with general terminal value and general random generator. Those …

The purpose of this thesis is to study a numerical method for backward doubly stochastic
differential equations (BDSDEs in short). In the last two decades, several methods were …

This document is a synthesis of the research that I have been conducting, along with my co–
authors, since the defense of my PhD thesis. This includes several topics, which are …

In this article, we propose a wellposedness theory for a class of second order backward
doubly stochastic differential equation (2BDSDE). We prove existence and uniqueness of …

We prove an L 2-regularity result for the solutions of Forward Backward doubly stochastic
differential equations (F-BDSDEs) under globally Lipschitz continuous assumptions on the …